Question

The number of carbon atoms per unit cell of diamond unit cell is

• A. 4
• B. 8
• C. 6
• D. 1

Answer 1

The Correct Option is B

To determine the number of carbon atoms in a diamond unit cell, we must understand the crystalline structure of diamond. Diamond is a crystal form of carbon, and its structure is known for its high symmetry and unique tetrahedral bonding of carbon atoms.

The diamond crystal structure is a cubic lattice that belongs to the space group of the face-centered cubic (FCC) lattice system, but it is more specifically a variant known as the diamond cubic structure.

1. The diamond structure can be viewed as two interpenetrating face-centered cubic (FCC) lattices, offset along the body diagonal by one-quarter of the diagonal.
2. In the face-centered cubic (FCC) lattice, each corner atom is shared by 8 adjacent unit cells, and each face-centered atom is shared by 2 unit cells.
3. A diamond unit cell consists of 8 atoms occupying each corner of the cube and additional atoms at the center of each face and along the internal body diagonal.
4. Therefore, the effective number of atoms per unit cell of diamond can be calculated as follows:

8 \times \frac{1}{8} + 6 \times \frac{1}{2} + 4 = 1 + 3 + 4 = 8

Thus, each diamond unit cell contains 8 carbon atoms. This number is essential in understanding the density and various properties of diamond.

Therefore, the correct answer is 8.